Fig. 3: Two-qubit operation of device A.

a,b, Probability of detecting an even spin state P_even after a microwave burst of fixed power and duration at different J gate voltages V_J when preparing a mixed odd state of \(| \downarrow \uparrow \rangle \) and \(| \uparrow \downarrow \rangle \) (a) and a pure even state \(| \downarrow \downarrow \rangle \) (b). The power and duration of the microwave burst are roughly calibrated to a single-qubit π rotation. The local oscillator frequency is set to f_LO = 18.610 GHz. The mixed odd state is initialized with a t_ramp = 1 μs ramp at V_J = 0.96 V over the anti-crossing and the even state with heralded initialization based on a t_ramp = 1 μs ramp at V_J = 1.12 V. All experiments throughout the paper were conducted with an even state \(| \downarrow \downarrow \rangle \) initialization, unless otherwise specified. c, Controlled phase (CZ) oscillation as a function of exchange time t_exchange and exchange gate voltage V_J. We apply dynamical decoupling by a consecutive π rotation on both qubits to filter out other phase-accumulating effects, such as Stark shift. d, Decoupled exchange oscillation fingerprint for fixed exchange time t_exchange = 10 μs as a function of plunger voltage detuning ΔV_P and exchange gate voltage V_J. The triangle indicates the exchange gate voltage used for the CZ gate. e, Exchange strength as a function of exchange gate voltage extracted from fitting exchange oscillations in c. The controllability is fitted assuming J_exchange ∝ a exp bV_J, resulting in a range between b = 9.78 dec V⁻¹ and 18.44 dec V⁻¹ across devices A–D. The variation in exchange controllability across the devices is probably due to fabrication variability. f,g, Calibration of the CZ single-qubit phase correction by preparing the target spin in superposition, applying a CPHASE followed by a virtual phase rotation for qubits 1 (f) and 2 (g)^4,7. Vertical lines indicate the phase values for which the spin state of Q1 (Q2) is flipped if Q2 (Q1) is in the on/spin-up state. The read-out probability is unscaled in all data.